Rows of the thermoelectric modules of Example 3.13 are attached to the flat absorber plate of Problem 3.108. The rows of modules are separated by L_sep 
= 0.5 m and the backs of the modules are cooled by water at a temperature of T_w  = 40°C, with h = 45 W/m₂ · K.

Determine the electric power produced by one row of thermoelectric modules connected in series electrically with a load resistance of 60Ω. Calculate the heat transfer rate to the flowing water. Assume rows of 20 immediately adjacent modules, with the lengths of both the module rows and water tubing to be L_row = 20W where W = 54 mm is the module dimension taken from Example 3.13. Neglect thermal contact resistances and the temperature drop across the tube wall, and assume that the high thermal conductivity tube wall creates a uniform temperature around the tube perimeter. Because of the thermal resistance provided by the thermoelectric modules, it is no longer appropriate to assume that the temperature of the absorber plate directly above a tube is equal to that of the water.

Example 3.13

An array of M = 48 thermoelectric modules is installed on the exhaust of a sports car. Each module has an effective Seebeck coefficient of S_p-n,eff =
0.1435 V/K, and an internal electrical resistance of R_e,eff = 4Ω. In addition, each module is of width and length W = 54 mm and contains N = 100 pairs of semiconducting pellets. Each pellet has an overall length of 2L = 5mm and cross-sectional area A_c,s = 1.2 10^-5 m² and is characterized by a thermal conductivity of k_s = 1.2 W/m
· K. The hot side of each module is exposed to exhaust gases at T_∞,1 = 550°C with h₁ = 40 W/m₂ · K, while the opposite side of each module is cooled by pressurized water at T_∞,2  = 105°C with h₂ = 500 W/m² · K. If the modules are wired in series, and the load resistance is R_e,load = 400Ω, what is the electric power harvested from the hot exhaust gases?

Transcribed Image Text:

w- Water Tw. h Insulation 9rad Lep Cover plate Evacuated space Absorber plate Thermoelectric module